Simplify the following expression: $\sqrt{2}+\sqrt{18}+\sqrt{32}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{2}+\sqrt{18}+\sqrt{32}$ $= \sqrt{2}+\sqrt{9 \cdot 2}+\sqrt{16 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{2}+\sqrt{9} \cdot \sqrt{2}+\sqrt{16} \cdot \sqrt{2}$ $= \sqrt{2}+3\sqrt{2}+4\sqrt{2}$ Finally, simplify by combining the terms. $= ( 1 + 3 + 4 )\sqrt{2} = 8\sqrt{2}$